AP STATISTICS

LESSON 1 – 2 (DAY 3)

LINEAR TRANSFORMATIONS AND COMPARING DISTRIBUTIONS

ESSENTIAL QUESTION:

How is the shape and spread effected by linear transformations?

Objective:  To transform data and find the effect on the shape and spread.

Linear Transformation

 A linear transformation changes the original variable x into the new variable x new equation of the form given by an x new = a + bx  Adding the constant a shifts all values of x upward or downward by the same amount.

 Multiplying by the positive constant b changes the size of the unit of measurement.

Exercise: Page 53 Example 1.15

LOS ANGELES LAKERS’ SALARIES

Effects of Linear Transformation

To see the effect of a linear transformation on measures of center and spread, apply these rules:  Multiplying each observation by a positive number b multiplies both measures of center (mean and median) and measures of spread ( standard deviation and IQR) by b.

 Adding the same number a ( either positive or negative to each observation adds a to measures of center and to quartiles but does not change measures of spread.

Exercises Pages 59 – 61 Exercises 1.47

: Get Your Hot Dogs Here!

Exercise 1.48

: Which AP Exam is Easier: Calculus AB or Statistics?

Exercise 1.49

: Who Makes More?

Exercise 1.50

: Basketball Playoff Scores

Page 57

Example 1.17

Swiss Doctors

Male doctors :  27, 50, 33, 25, 86, 25, 86, 25, 85, 31, 37, 44, 20, 36, 59, 34, 28 Female doctors :  5, 7, 10, 14, 18, 19, 25, 29, 31, 33